A box has a square bottom. The height has not yet been determined, but the bottom is 10 inches by 10 inches. The volume formula is V = lwh, because each of the length and width is 10, lw becomes 10 – 10 = 100.
The formula
for the box’s volume is V = 100h.
(a) If
the height of the box is to be 6 inches, what is its volume?
(b) If
the volume is to be 450 cubic inches, what should its height be?
(c) If
the volume is to be 825 cubic inches, what should its height be?
Answer
(a) The
height is 6 inches, so h = 6. Then V = 100h becomes V ¼
100(6)
= 600.
The
box’s volume is 600 cubic inches.
(b) The
volume is 450 cubic inches, so V = 450, and V ¼ 100h becomes 450 ¼ 100h.
The
box’s height would need to be 4.5 inches.
(c) The
volume is 825, so V = 100h becomes 825 = 100h.
The
height should be 8.25 inches.
Suppose a square
has a perimeter of 18 cm. What is the length of each of its sides? (Recall the
formula for the perimeter of a square: P = 4l where l is the length of each of
its sides.)
The length
of each of its sides is 4.5 cm.
The
relationship between degrees Fahrenheit and degrees Celsius is given by the
formula 
.
At what temperature will degrees Fahrenheit
and degrees Celsius be the same? Both expressions ‘‘C’’ and ‘‘
’’ represent degrees Celsius, so
when Fahrenheit equals Celsius, we can say that . Before, our equation had two
variables. By substituting ‘‘’’ in place of ‘‘C,’’ we have
reduced the number of variables in the equation to one. Now we can solve it.
The LCD is
9.
At –40
degrees Fahrenheit and degrees Celsius are the same.
Practice
1. The daily charge for a small rental car is C = 18
+ 0.35x where x is the number of miles driven.
(a) If
the car was driven 80 miles, what was the charge?
(b) Suppose
that a day’s bill was $39. How many miles were driven?
2. The profit obtained for a company’s product is
given by P = 25x – 8150, where P is the profit in dollars and x is the number of
units sold. How many units must be sold in order for the company to have a
profit of $5000 from this product?
3. A salesman’s weekly salary is based on the
formula S = 200 + 0.10s, where S is the week’s salary in dollars and s is the week’s
sales level in dollars. One week, his salary was $410. What was the sales level
for that week?
4. The volume of a box with a rectangular bottom is
given by V = 120h, where V is the volume in cubic inches and h is the height in
inches. If the volume of the box is to be 1140 cubic inches, what should its
height be?
5. The volume of a certain cylinder with radius 2.8
cm is given by V = 7.84 πh, where h is the height of the cylinder in
centimeters. If the volume needs to be 25.088π cubic centimeters, what does the
height need to be?
6. At what temperature will the Celsius reading be
twice as high as the Fahrenheit reading?
7. At what temperature will degrees Fahrenheit be
twice degrees Celsius?
Solutions
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